Galerkin’s method to solve a fractional time-delayed jerk oscillator

An immediate analytic solution for the time-delayed fractional linear jerk oscillator is derived in the present study. The currently used method adheres to basic, easily implementable criteria. This proposed approach is based on transforming the time-delayed fractional oscillator to an equivalent os...

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Bibliographic Details
Published in:Archive of applied mechanics (1991) 2023-09, Vol.93 (9), p.3597-3607
Main Authors: El-Dib, Yusry O., Elgazery, Nasser S., Alyousef, Haifa A.
Format: Article
Language:English
Subjects:
Classical Mechanics
Engineering
Equivalence
Exact solutions
Galerkin method
Mathematical analysis
Original
Oscillators
Stability analysis
Theoretical and Applied Mechanics
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Summary:An immediate analytic solution for the time-delayed fractional linear jerk oscillator is derived in the present study. The currently used method adheres to basic, easily implementable criteria. This proposed approach is based on transforming the time-delayed fractional oscillator to an equivalent oscillator with ordinary derivatives, which makes the solution procedure simple. The conversion process steps to an equivalent ordinary differential oscillator are displayed. Galerkin’s method is used to derive the jerk frequency. The good match between the analytic and numerical outcomes shows that the equivalent linearized mechanism leads to finding a satisfying and accurate solution. Stability discussion is conducted analytically and numerically.
ISSN:0939-1533
1432-0681
DOI:10.1007/s00419-023-02455-8